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The circular polarizer is composed of a linear polarizer and a quarter-wave plate, which is made of a special birefringent material.

The optical properties of the birefringence are when the light will have two different directions of refraction. And the wave plate itself according to its own material has the so-called optical axis, when a linearly polarized light into his vibration will be broken down into two directions of vibration: one is the direction of the optical axis, known as the fast axis, The other is the direction perpendicular to the optical axis, called the slow axis.

When the linearly polarized light and the optical axis of the quarter-wave plate are parallel or vertical (the angle is 0 degrees or 90 degrees), the amplitude of the other direction is zero and the original linearly polarized light is maintained.

It is not broken down into two directions. And when the angle between the linearly polarized light and the optical axis is 45 degrees, the amplitude of the two directions is equal and the so-called circularly polarized light is formed; but if it is other angles, the amplitude of the two directions is different, And become elliptically polarized light. So in fact, circular polarization and linear polarization can be regarded as a special case of elliptical polarization.

In addition to the wave of light will be divided into two directions of vibration, vibration in these two directions because of the different thickness of the wave plate, there are different phase difference; and in the circular polarizer on the quarter of the wave plate.

That is, will produce a quarter of the phase difference. But also because of this quarter of the phase difference, so in the fast axis and slow axis of the two directions of the wave synthesis, it will produce a vibration direction will rotate the wave.

Circularly polarized light is in a polarization state in which, at each point, the electric field vector has a constant magnitude, but its direction rotates with time at a steady rate in a plane perpendicular to the direction of the wave traveling.

Circularly polarized light can be produced by passing linearly polarized light through a quarter wave plate (or retarder).

Depending on the orientation of the quarter waveplate with respect to the electric field vector of the linearly polarized light, the final circularly polarized light can be in one of two possible states, right circular polarization in which the electric field vector rotates in a right-hand orientation with respect to the direction of propagation, and left circular polarization in which the vector rotates in a left-hand orientation.

Waveplates, also known as retarders, transmit light and modify its polarization state by retarding (or delaying) one component of polarization with respect to its orthogonal component.

When unpolarized light passes through a wave plate, the waveplate is equivalent to a window, light remains unpolarized.

However, when a linearly polarized light passes through a wave plate, the orientation of the polarized light will be changed.

The most commonly used wave plates are the half wave plate (1/2 λ) and the quarter wave plate (1/4 λ).

Birefringence - Waveplates are made from birefringent materials in which light splits into two different paths, each path has its own index of refraction.

The component in the smaller index (fast axis) of refraction travels faster than that in the larger index of refraction (slow axis).

In addition, the electric field vectors of both components are perpendicular to each other.

The difference in the speeds of light in these two axes (called retardation) causes phase shift.

Retardation can be measured in degrees, radians or wavelength.
Quarter-wave plates are used to turn a linearly polarized light into circularly polarized light and vice versa.

If the electric field vectors of the linearly polarized light form 45° to the fast axis or the slow axis of a quarter wave plate (¼ λ), equal amounts of light intensity can pass through the wave plate as shown in Figure 10, As a result, when the wave at one point where the fast polarized component is at maximum, the slow polarized component is zero.

Due to the 45° phase shift between these two components, a circularly polarized light is produced.

As stated earlier, the circular polarization can be either left-handed or right handed depends on the electric field at 45° to the left or to the right of the fast axis of the wave plate.

A quarter wave plate separates an electric field vector into two equal components.